// The MIT License (MIT)
// Copyright (c) 2014 Matthew Klingensmith and Ivan Dryanovski
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.

#include "MarchingCubes.h"

namespace chisel
{
    // Lookup table from the 256 possible cube configurations from
    // CalculateVertexConfigurationIndex() to the 0-5 triplets the give the edges
    // where the triangle vertices lie.
    int MarchingCubes::triangleTable[256][16] =
    {
            { -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  0,  8,  3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  0,  1,  9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  1,  8,  3,  9,  8,  1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  1,  2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  0,  8,  3,  1,  2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  9,  2, 10,  0,  2,  9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  2,  8,  3,  2, 10,  8, 10,  9,  8, -1, -1, -1, -1, -1, -1, -1 },
            {  3, 11,  2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  0, 11,  2,  8, 11,  0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  1,  9,  0,  2,  3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  1, 11,  2,  1,  9, 11,  9,  8, 11, -1, -1, -1, -1, -1, -1, -1 },
            {  3, 10,  1, 11, 10,  3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  0, 10,  1,  0,  8, 10,  8, 11, 10, -1, -1, -1, -1, -1, -1, -1 },
            {  3,  9,  0,  3, 11,  9, 11, 10,  9, -1, -1, -1, -1, -1, -1, -1 },
            {  9,  8, 10, 10,  8, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  4,  7,  8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  4,  3,  0,  7,  3,  4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  0,  1,  9,  8,  4,  7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  4,  1,  9,  4,  7,  1,  7,  3,  1, -1, -1, -1, -1, -1, -1, -1 },
            {  1,  2, 10,  8,  4,  7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  3,  4,  7,  3,  0,  4,  1,  2, 10, -1, -1, -1, -1, -1, -1, -1 },
            {  9,  2, 10,  9,  0,  2,  8,  4,  7, -1, -1, -1, -1, -1, -1, -1 },
            {  2, 10,  9,  2,  9,  7,  2,  7,  3,  7,  9,  4, -1, -1, -1, -1 },
            {  8,  4,  7,  3, 11,  2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            { 11,  4,  7, 11,  2,  4,  2,  0,  4, -1, -1, -1, -1, -1, -1, -1 },
            {  9,  0,  1,  8,  4,  7,  2,  3, 11, -1, -1, -1, -1, -1, -1, -1 },
            {  4,  7, 11,  9,  4, 11,  9, 11,  2,  9,  2,  1, -1, -1, -1, -1 },
            {  3, 10,  1,  3, 11, 10,  7,  8,  4, -1, -1, -1, -1, -1, -1, -1 },
            {  1, 11, 10,  1,  4, 11,  1,  0,  4,  7, 11,  4, -1, -1, -1, -1 },
            {  4,  7,  8,  9,  0, 11,  9, 11, 10, 11,  0,  3, -1, -1, -1, -1 },
            {  4,  7, 11,  4, 11,  9,  9, 11, 10, -1, -1, -1, -1, -1, -1, -1 },
            {  9,  5,  4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  9,  5,  4,  0,  8,  3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  0,  5,  4,  1,  5,  0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  8,  5,  4,  8,  3,  5,  3,  1,  5, -1, -1, -1, -1, -1, -1, -1 },
            {  1,  2, 10,  9,  5,  4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  3,  0,  8,  1,  2, 10,  4,  9,  5, -1, -1, -1, -1, -1, -1, -1 },
            {  5,  2, 10,  5,  4,  2,  4,  0,  2, -1, -1, -1, -1, -1, -1, -1 },
            {  2, 10,  5,  3,  2,  5,  3,  5,  4,  3,  4,  8, -1, -1, -1, -1 },
            {  9,  5,  4,  2,  3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  0, 11,  2,  0,  8, 11,  4,  9,  5, -1, -1, -1, -1, -1, -1, -1 },
            {  0,  5,  4,  0,  1,  5,  2,  3, 11, -1, -1, -1, -1, -1, -1, -1 },
            {  2,  1,  5,  2,  5,  8,  2,  8, 11,  4,  8,  5, -1, -1, -1, -1 },
            { 10,  3, 11, 10,  1,  3,  9,  5,  4, -1, -1, -1, -1, -1, -1, -1 },
            {  4,  9,  5,  0,  8,  1,  8, 10,  1,  8, 11, 10, -1, -1, -1, -1 },
            {  5,  4,  0,  5,  0, 11,  5, 11, 10, 11,  0,  3, -1, -1, -1, -1 },
            {  5,  4,  8,  5,  8, 10, 10,  8, 11, -1, -1, -1, -1, -1, -1, -1 },
            {  9,  7,  8,  5,  7,  9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  9,  3,  0,  9,  5,  3,  5,  7,  3, -1, -1, -1, -1, -1, -1, -1 },
            {  0,  7,  8,  0,  1,  7,  1,  5,  7, -1, -1, -1, -1, -1, -1, -1 },
            {  1,  5,  3,  3,  5,  7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  9,  7,  8,  9,  5,  7, 10,  1,  2, -1, -1, -1, -1, -1, -1, -1 },
            { 10,  1,  2,  9,  5,  0,  5,  3,  0,  5,  7,  3, -1, -1, -1, -1 },
            {  8,  0,  2,  8,  2,  5,  8,  5,  7, 10,  5,  2, -1, -1, -1, -1 },
            {  2, 10,  5,  2,  5,  3,  3,  5,  7, -1, -1, -1, -1, -1, -1, -1 },
            {  7,  9,  5,  7,  8,  9,  3, 11,  2, -1, -1, -1, -1, -1, -1, -1 },
            {  9,  5,  7,  9,  7,  2,  9,  2,  0,  2,  7, 11, -1, -1, -1, -1 },
            {  2,  3, 11,  0,  1,  8,  1,  7,  8,  1,  5,  7, -1, -1, -1, -1 },
            { 11,  2,  1, 11,  1,  7,  7,  1,  5, -1, -1, -1, -1, -1, -1, -1 },
            {  9,  5,  8,  8,  5,  7, 10,  1,  3, 10,  3, 11, -1, -1, -1, -1 },
            {  5,  7,  0,  5,  0,  9,  7, 11,  0,  1,  0, 10, 11, 10,  0, -1 },
            { 11, 10,  0, 11,  0,  3, 10,  5,  0,  8,  0,  7,  5,  7,  0, -1 },
            { 11, 10,  5,  7, 11,  5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            { 10,  6,  5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  0,  8,  3,  5, 10,  6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  9,  0,  1,  5, 10,  6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  1,  8,  3,  1,  9,  8,  5, 10,  6, -1, -1, -1, -1, -1, -1, -1 },
            {  1,  6,  5,  2,  6,  1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  1,  6,  5,  1,  2,  6,  3,  0,  8, -1, -1, -1, -1, -1, -1, -1 },
            {  9,  6,  5,  9,  0,  6,  0,  2,  6, -1, -1, -1, -1, -1, -1, -1 },
            {  5,  9,  8,  5,  8,  2,  5,  2,  6,  3,  2,  8, -1, -1, -1, -1 },
            {  2,  3, 11, 10,  6,  5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            { 11,  0,  8, 11,  2,  0, 10,  6,  5, -1, -1, -1, -1, -1, -1, -1 },
            {  0,  1,  9,  2,  3, 11,  5, 10,  6, -1, -1, -1, -1, -1, -1, -1 },
            {  5, 10,  6,  1,  9,  2,  9, 11,  2,  9,  8, 11, -1, -1, -1, -1 },
            {  6,  3, 11,  6,  5,  3,  5,  1,  3, -1, -1, -1, -1, -1, -1, -1 },
            {  0,  8, 11,  0, 11,  5,  0,  5,  1,  5, 11,  6, -1, -1, -1, -1 },
            {  3, 11,  6,  0,  3,  6,  0,  6,  5,  0,  5,  9, -1, -1, -1, -1 },
            {  6,  5,  9,  6,  9, 11, 11,  9,  8, -1, -1, -1, -1, -1, -1, -1 },
            {  5, 10,  6,  4,  7,  8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  4,  3,  0,  4,  7,  3,  6,  5, 10, -1, -1, -1, -1, -1, -1, -1 },
            {  1,  9,  0,  5, 10,  6,  8,  4,  7, -1, -1, -1, -1, -1, -1, -1 },
            { 10,  6,  5,  1,  9,  7,  1,  7,  3,  7,  9,  4, -1, -1, -1, -1 },
            {  6,  1,  2,  6,  5,  1,  4,  7,  8, -1, -1, -1, -1, -1, -1, -1 },
            {  1,  2,  5,  5,  2,  6,  3,  0,  4,  3,  4,  7, -1, -1, -1, -1 },
            {  8,  4,  7,  9,  0,  5,  0,  6,  5,  0,  2,  6, -1, -1, -1, -1 },
            {  7,  3,  9,  7,  9,  4,  3,  2,  9,  5,  9,  6,  2,  6,  9, -1 },
            {  3, 11,  2,  7,  8,  4, 10,  6,  5, -1, -1, -1, -1, -1, -1, -1 },
            {  5, 10,  6,  4,  7,  2,  4,  2,  0,  2,  7, 11, -1, -1, -1, -1 },
            {  0,  1,  9,  4,  7,  8,  2,  3, 11,  5, 10,  6, -1, -1, -1, -1 },
            {  9,  2,  1,  9, 11,  2,  9,  4, 11,  7, 11,  4,  5, 10,  6, -1 },
            {  8,  4,  7,  3, 11,  5,  3,  5,  1,  5, 11,  6, -1, -1, -1, -1 },
            {  5,  1, 11,  5, 11,  6,  1,  0, 11,  7, 11,  4,  0,  4, 11, -1 },
            {  0,  5,  9,  0,  6,  5,  0,  3,  6, 11,  6,  3,  8,  4,  7, -1 },
            {  6,  5,  9,  6,  9, 11,  4,  7,  9,  7, 11,  9, -1, -1, -1, -1 },
            { 10,  4,  9,  6,  4, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  4, 10,  6,  4,  9, 10,  0,  8,  3, -1, -1, -1, -1, -1, -1, -1 },
            { 10,  0,  1, 10,  6,  0,  6,  4,  0, -1, -1, -1, -1, -1, -1, -1 },
            {  8,  3,  1,  8,  1,  6,  8,  6,  4,  6,  1, 10, -1, -1, -1, -1 },
            {  1,  4,  9,  1,  2,  4,  2,  6,  4, -1, -1, -1, -1, -1, -1, -1 },
            {  3,  0,  8,  1,  2,  9,  2,  4,  9,  2,  6,  4, -1, -1, -1, -1 },
            {  0,  2,  4,  4,  2,  6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  8,  3,  2,  8,  2,  4,  4,  2,  6, -1, -1, -1, -1, -1, -1, -1 },
            { 10,  4,  9, 10,  6,  4, 11,  2,  3, -1, -1, -1, -1, -1, -1, -1 },
            {  0,  8,  2,  2,  8, 11,  4,  9, 10,  4, 10,  6, -1, -1, -1, -1 },
            {  3, 11,  2,  0,  1,  6,  0,  6,  4,  6,  1, 10, -1, -1, -1, -1 },
            {  6,  4,  1,  6,  1, 10,  4,  8,  1,  2,  1, 11,  8, 11,  1, -1 },
            {  9,  6,  4,  9,  3,  6,  9,  1,  3, 11,  6,  3, -1, -1, -1, -1 },
            {  8, 11,  1,  8,  1,  0, 11,  6,  1,  9,  1,  4,  6,  4,  1, -1 },
            {  3, 11,  6,  3,  6,  0,  0,  6,  4, -1, -1, -1, -1, -1, -1, -1 },
            {  6,  4,  8, 11,  6,  8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  7, 10,  6,  7,  8, 10,  8,  9, 10, -1, -1, -1, -1, -1, -1, -1 },
            {  0,  7,  3,  0, 10,  7,  0,  9, 10,  6,  7, 10, -1, -1, -1, -1 },
            { 10,  6,  7,  1, 10,  7,  1,  7,  8,  1,  8,  0, -1, -1, -1, -1 },
            { 10,  6,  7, 10,  7,  1,  1,  7,  3, -1, -1, -1, -1, -1, -1, -1 },
            {  1,  2,  6,  1,  6,  8,  1,  8,  9,  8,  6,  7, -1, -1, -1, -1 },
            {  2,  6,  9,  2,  9,  1,  6,  7,  9,  0,  9,  3,  7,  3,  9, -1 },
            {  7,  8,  0,  7,  0,  6,  6,  0,  2, -1, -1, -1, -1, -1, -1, -1 },
            {  7,  3,  2,  6,  7,  2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  2,  3, 11, 10,  6,  8, 10,  8,  9,  8,  6,  7, -1, -1, -1, -1 },
            {  2,  0,  7,  2,  7, 11,  0,  9,  7,  6,  7, 10,  9, 10,  7, -1 },
            {  1,  8,  0,  1,  7,  8,  1, 10,  7,  6,  7, 10,  2,  3, 11, -1 },
            { 11,  2,  1, 11,  1,  7, 10,  6,  1,  6,  7,  1, -1, -1, -1, -1 },
            {  8,  9,  6,  8,  6,  7,  9,  1,  6, 11,  6,  3,  1,  3,  6, -1 },
            {  0,  9,  1, 11,  6,  7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  7,  8,  0,  7,  0,  6,  3, 11,  0, 11,  6,  0, -1, -1, -1, -1 },
            {  7, 11,  6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  7,  6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  3,  0,  8, 11,  7,  6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  0,  1,  9, 11,  7,  6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  8,  1,  9,  8,  3,  1, 11,  7,  6, -1, -1, -1, -1, -1, -1, -1 },
            { 10,  1,  2,  6, 11,  7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  1,  2, 10,  3,  0,  8,  6, 11,  7, -1, -1, -1, -1, -1, -1, -1 },
            {  2,  9,  0,  2, 10,  9,  6, 11,  7, -1, -1, -1, -1, -1, -1, -1 },
            {  6, 11,  7,  2, 10,  3, 10,  8,  3, 10,  9,  8, -1, -1, -1, -1 },
            {  7,  2,  3,  6,  2,  7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  7,  0,  8,  7,  6,  0,  6,  2,  0, -1, -1, -1, -1, -1, -1, -1 },
            {  2,  7,  6,  2,  3,  7,  0,  1,  9, -1, -1, -1, -1, -1, -1, -1 },
            {  1,  6,  2,  1,  8,  6,  1,  9,  8,  8,  7,  6, -1, -1, -1, -1 },
            { 10,  7,  6, 10,  1,  7,  1,  3,  7, -1, -1, -1, -1, -1, -1, -1 },
            { 10,  7,  6,  1,  7, 10,  1,  8,  7,  1,  0,  8, -1, -1, -1, -1 },
            {  0,  3,  7,  0,  7, 10,  0, 10,  9,  6, 10,  7, -1, -1, -1, -1 },
            {  7,  6, 10,  7, 10,  8,  8, 10,  9, -1, -1, -1, -1, -1, -1, -1 },
            {  6,  8,  4, 11,  8,  6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  3,  6, 11,  3,  0,  6,  0,  4,  6, -1, -1, -1, -1, -1, -1, -1 },
            {  8,  6, 11,  8,  4,  6,  9,  0,  1, -1, -1, -1, -1, -1, -1, -1 },
            {  9,  4,  6,  9,  6,  3,  9,  3,  1, 11,  3,  6, -1, -1, -1, -1 },
            {  6,  8,  4,  6, 11,  8,  2, 10,  1, -1, -1, -1, -1, -1, -1, -1 },
            {  1,  2, 10,  3,  0, 11,  0,  6, 11,  0,  4,  6, -1, -1, -1, -1 },
            {  4, 11,  8,  4,  6, 11,  0,  2,  9,  2, 10,  9, -1, -1, -1, -1 },
            { 10,  9,  3, 10,  3,  2,  9,  4,  3, 11,  3,  6,  4,  6,  3, -1 },
            {  8,  2,  3,  8,  4,  2,  4,  6,  2, -1, -1, -1, -1, -1, -1, -1 },
            {  0,  4,  2,  4,  6,  2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  1,  9,  0,  2,  3,  4,  2,  4,  6,  4,  3,  8, -1, -1, -1, -1 },
            {  1,  9,  4,  1,  4,  2,  2,  4,  6, -1, -1, -1, -1, -1, -1, -1 },
            {  8,  1,  3,  8,  6,  1,  8,  4,  6,  6, 10,  1, -1, -1, -1, -1 },
            { 10,  1,  0, 10,  0,  6,  6,  0,  4, -1, -1, -1, -1, -1, -1, -1 },
            {  4,  6,  3,  4,  3,  8,  6, 10,  3,  0,  3,  9, 10,  9,  3, -1 },
            { 10,  9,  4,  6, 10,  4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  4,  9,  5,  7,  6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  0,  8,  3,  4,  9,  5, 11,  7,  6, -1, -1, -1, -1, -1, -1, -1 },
            {  5,  0,  1,  5,  4,  0,  7,  6, 11, -1, -1, -1, -1, -1, -1, -1 },
            { 11,  7,  6,  8,  3,  4,  3,  5,  4,  3,  1,  5, -1, -1, -1, -1 },
            {  9,  5,  4, 10,  1,  2,  7,  6, 11, -1, -1, -1, -1, -1, -1, -1 },
            {  6, 11,  7,  1,  2, 10,  0,  8,  3,  4,  9,  5, -1, -1, -1, -1 },
            {  7,  6, 11,  5,  4, 10,  4,  2, 10,  4,  0,  2, -1, -1, -1, -1 },
            {  3,  4,  8,  3,  5,  4,  3,  2,  5, 10,  5,  2, 11,  7,  6, -1 },
            {  7,  2,  3,  7,  6,  2,  5,  4,  9, -1, -1, -1, -1, -1, -1, -1 },
            {  9,  5,  4,  0,  8,  6,  0,  6,  2,  6,  8,  7, -1, -1, -1, -1 },
            {  3,  6,  2,  3,  7,  6,  1,  5,  0,  5,  4,  0, -1, -1, -1, -1 },
            {  6,  2,  8,  6,  8,  7,  2,  1,  8,  4,  8,  5,  1,  5,  8, -1 },
            {  9,  5,  4, 10,  1,  6,  1,  7,  6,  1,  3,  7, -1, -1, -1, -1 },
            {  1,  6, 10,  1,  7,  6,  1,  0,  7,  8,  7,  0,  9,  5,  4, -1 },
            {  4,  0, 10,  4, 10,  5,  0,  3, 10,  6, 10,  7,  3,  7, 10, -1 },
            {  7,  6, 10,  7, 10,  8,  5,  4, 10,  4,  8, 10, -1, -1, -1, -1 },
            {  6,  9,  5,  6, 11,  9, 11,  8,  9, -1, -1, -1, -1, -1, -1, -1 },
            {  3,  6, 11,  0,  6,  3,  0,  5,  6,  0,  9,  5, -1, -1, -1, -1 },
            {  0, 11,  8,  0,  5, 11,  0,  1,  5,  5,  6, 11, -1, -1, -1, -1 },
            {  6, 11,  3,  6,  3,  5,  5,  3,  1, -1, -1, -1, -1, -1, -1, -1 },
            {  1,  2, 10,  9,  5, 11,  9, 11,  8, 11,  5,  6, -1, -1, -1, -1 },
            {  0, 11,  3,  0,  6, 11,  0,  9,  6,  5,  6,  9,  1,  2, 10, -1 },
            { 11,  8,  5, 11,  5,  6,  8,  0,  5, 10,  5,  2,  0,  2,  5, -1 },
            {  6, 11,  3,  6,  3,  5,  2, 10,  3, 10,  5,  3, -1, -1, -1, -1 },
            {  5,  8,  9,  5,  2,  8,  5,  6,  2,  3,  8,  2, -1, -1, -1, -1 },
            {  9,  5,  6,  9,  6,  0,  0,  6,  2, -1, -1, -1, -1, -1, -1, -1 },
            {  1,  5,  8,  1,  8,  0,  5,  6,  8,  3,  8,  2,  6,  2,  8, -1 },
            {  1,  5,  6,  2,  1,  6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  1,  3,  6,  1,  6, 10,  3,  8,  6,  5,  6,  9,  8,  9,  6, -1 },
            { 10,  1,  0, 10,  0,  6,  9,  5,  0,  5,  6,  0, -1, -1, -1, -1 },
            {  0,  3,  8,  5,  6, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            { 10,  5,  6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            { 11,  5, 10,  7,  5, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            { 11,  5, 10, 11,  7,  5,  8,  3,  0, -1, -1, -1, -1, -1, -1, -1 },
            {  5, 11,  7,  5, 10, 11,  1,  9,  0, -1, -1, -1, -1, -1, -1, -1 },
            { 10,  7,  5, 10, 11,  7,  9,  8,  1,  8,  3,  1, -1, -1, -1, -1 },
            { 11,  1,  2, 11,  7,  1,  7,  5,  1, -1, -1, -1, -1, -1, -1, -1 },
            {  0,  8,  3,  1,  2,  7,  1,  7,  5,  7,  2, 11, -1, -1, -1, -1 },
            {  9,  7,  5,  9,  2,  7,  9,  0,  2,  2, 11,  7, -1, -1, -1, -1 },
            {  7,  5,  2,  7,  2, 11,  5,  9,  2,  3,  2,  8,  9,  8,  2, -1 },
            {  2,  5, 10,  2,  3,  5,  3,  7,  5, -1, -1, -1, -1, -1, -1, -1 },
            {  8,  2,  0,  8,  5,  2,  8,  7,  5, 10,  2,  5, -1, -1, -1, -1 },
            {  9,  0,  1,  5, 10,  3,  5,  3,  7,  3, 10,  2, -1, -1, -1, -1 },
            {  9,  8,  2,  9,  2,  1,  8,  7,  2, 10,  2,  5,  7,  5,  2, -1 },
            {  1,  3,  5,  3,  7,  5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  0,  8,  7,  0,  7,  1,  1,  7,  5, -1, -1, -1, -1, -1, -1, -1 },
            {  9,  0,  3,  9,  3,  5,  5,  3,  7, -1, -1, -1, -1, -1, -1, -1 },
            {  9,  8,  7,  5,  9,  7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  5,  8,  4,  5, 10,  8, 10, 11,  8, -1, -1, -1, -1, -1, -1, -1 },
            {  5,  0,  4,  5, 11,  0,  5, 10, 11, 11,  3,  0, -1, -1, -1, -1 },
            {  0,  1,  9,  8,  4, 10,  8, 10, 11, 10,  4,  5, -1, -1, -1, -1 },
            { 10, 11,  4, 10,  4,  5, 11,  3,  4,  9,  4,  1,  3,  1,  4, -1 },
            {  2,  5,  1,  2,  8,  5,  2, 11,  8,  4,  5,  8, -1, -1, -1, -1 },
            {  0,  4, 11,  0, 11,  3,  4,  5, 11,  2, 11,  1,  5,  1, 11, -1 },
            {  0,  2,  5,  0,  5,  9,  2, 11,  5,  4,  5,  8, 11,  8,  5, -1 },
            {  9,  4,  5,  2, 11,  3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  2,  5, 10,  3,  5,  2,  3,  4,  5,  3,  8,  4, -1, -1, -1, -1 },
            {  5, 10,  2,  5,  2,  4,  4,  2,  0, -1, -1, -1, -1, -1, -1, -1 },
            {  3, 10,  2,  3,  5, 10,  3,  8,  5,  4,  5,  8,  0,  1,  9, -1 },
            {  5, 10,  2,  5,  2,  4,  1,  9,  2,  9,  4,  2, -1, -1, -1, -1 },
            {  8,  4,  5,  8,  5,  3,  3,  5,  1, -1, -1, -1, -1, -1, -1, -1 },
            {  0,  4,  5,  1,  0,  5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  8,  4,  5,  8,  5,  3,  9,  0,  5,  0,  3,  5, -1, -1, -1, -1 },
            {  9,  4,  5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  4, 11,  7,  4,  9, 11,  9, 10, 11, -1, -1, -1, -1, -1, -1, -1 },
            {  0,  8,  3,  4,  9,  7,  9, 11,  7,  9, 10, 11, -1, -1, -1, -1 },
            {  1, 10, 11,  1, 11,  4,  1,  4,  0,  7,  4, 11, -1, -1, -1, -1 },
            {  3,  1,  4,  3,  4,  8,  1, 10,  4,  7,  4, 11, 10, 11,  4, -1 },
            {  4, 11,  7,  9, 11,  4,  9,  2, 11,  9,  1,  2, -1, -1, -1, -1 },
            {  9,  7,  4,  9, 11,  7,  9,  1, 11,  2, 11,  1,  0,  8,  3, -1 },
            { 11,  7,  4, 11,  4,  2,  2,  4,  0, -1, -1, -1, -1, -1, -1, -1 },
            { 11,  7,  4, 11,  4,  2,  8,  3,  4,  3,  2,  4, -1, -1, -1, -1 },
            {  2,  9, 10,  2,  7,  9,  2,  3,  7,  7,  4,  9, -1, -1, -1, -1 },
            {  9, 10,  7,  9,  7,  4, 10,  2,  7,  8,  7,  0,  2,  0,  7, -1 },
            {  3,  7, 10,  3, 10,  2,  7,  4, 10,  1, 10,  0,  4,  0, 10, -1 },
            {  1, 10,  2,  8,  7,  4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  4,  9,  1,  4,  1,  7,  7,  1,  3, -1, -1, -1, -1, -1, -1, -1 },
            {  4,  9,  1,  4,  1,  7,  0,  8,  1,  8,  7,  1, -1, -1, -1, -1 },
            {  4,  0,  3,  7,  4,  3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  4,  8,  7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  9, 10,  8, 10, 11,  8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  3,  0,  9,  3,  9, 11, 11,  9, 10, -1, -1, -1, -1, -1, -1, -1 },
            {  0,  1, 10,  0, 10,  8,  8, 10, 11, -1, -1, -1, -1, -1, -1, -1 },
            {  3,  1, 10, 11,  3, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  1,  2, 11,  1, 11,  9,  9, 11,  8, -1, -1, -1, -1, -1, -1, -1 },
            {  3,  0,  9,  3,  9, 11,  1,  2,  9,  2, 11,  9, -1, -1, -1, -1 },
            {  0,  2, 11,  8,  0, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  3,  2, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  2,  3,  8,  2,  8, 10, 10,  8,  9, -1, -1, -1, -1, -1, -1, -1 },
            {  9, 10,  2,  0,  9,  2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  2,  3,  8,  2,  8, 10,  0,  1,  8,  1, 10,  8, -1, -1, -1, -1 },
            {  1, 10,  2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  1,  3,  8,  9,  1,  8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  0,  9,  1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            {  0,  3,  8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
            { -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 }
    };

    // Lookup table from the 12 cube edge indices to their corresponding corner
    // indices.
    int MarchingCubes::edgeIndexPairs[12][2] =
    {
        { 0, 1 },
        { 1, 2 },
        { 2, 3 },
        { 3, 0 },
        { 4, 5 },
        { 5, 6 },
        { 6, 7 },
        { 7, 4 },
        { 0, 4 },
        { 1, 5 },
        { 2, 6 },
        { 3, 7 }
    };


    MarchingCubes::MarchingCubes()
    {
        // TODO Auto-generated constructor stub

    }

    MarchingCubes::~MarchingCubes()
    {
        // TODO Auto-generated destructor stub
    }

} // namespace chisel 
